Bolstered by the return of Marcus Smart and Al Horford, who both missed Tuesday's 118-107 game one drubbing, Boston were a team transformed as they squared the best-of-seven series 1-1.
Boston made only 11-of-34 from three-point range in Tuesday's lopsided opener, when Miami out-hustled them to claim a decisive victory.
But the Celtics shrugged off that misfiring performance in emphatic fashion, draining 20-of-40 from beyond the arc to overwhelm Miami.
Tatum led the scorers but there were huge contributions throughout the Celtics lineup.
Smart finished with 24 points, 12 assists and nine rebounds, while Jaylen Brown also posted 24 points, including 12 from three-point range.
Grant Williams added 19 from the bench, while Horford and Payton Pritchard had 10 points each.
Jimmy Butler led the Miami scoring with 29 points but only three other Heat players made double figures.
Celtics coach Ime Udoka said the return of Smart and Horford had been decisive.
"It was great to have them back, they're a calming presence," Udoka said.
"I don't think we played as poorly as the last game suggested. We won three quarters of that game but we saw a lot of positives and areas that we could attack."
Smart admitted he had found it hard to sit out game one with a foot injury.
"I felt bad that I couldn't be out there with my team-mates going to battle with them," Smart said.
"We're playing a really good Miami team and it's a blessing to be on the same court going to war. It was tough having to watch it."
- 'They embarrassed us' -
Miami coach Erik Spoelstra said his team had expected a Boston backlash.
"I'm sure they weren't happy about us putting up 118 against them in game one," Spoelstra said.
"When you get to this stage of the conference finals, you just have very good teams, teams without many weaknesses.
"It's great competition. But this only counts as one game. We don't like it. We just have to figure some things out."
Butler said he hoped the defeat would motivate Miami for game three.
"They tried to embarrass us, and they did embarrass us," Butler said.
A wild first quarter saw Miami pick up where they left off in game one, with Max Strus hitting back-to-back three-pointers to leave the Heat ahead by 10 points at 18-8.
But Boston produced a scintillating 17-0 run to turn the quarter on its head, with their long-range shooting vastly improved.
Brown knocked down a trio of three-pointers in the first period to leave the Celtics up by 35-24 heading into the second quarter.
The Celtics' shooting clinic continued in the second quarter, with Pritchard nailing a 26-foot three-pointer to put Boston 19 points clear at 47-28 midway through the period.
A Tatum three-pointer and two free throws soon afterwards left Boston 27 points clear at 64-37 and shortly afterwards the Celtics had built a 29-point lead when Grant Williams' driving layup made it 68-39.
Smart put the seal on a devastating first-half display with a pullup jump shot to make it 70-45 at half-time.
Miami rallied late in the third quarter and cut the Boston lead to 17 points at one stage, but the Celtics regrouped and again pulled away.
A three-pointer from Tatum took them 25 points clear in the closing seconds of the third quarter at 94-69, a lead which they held going into the final quarter.
Smart made it a 30-point lead early in the fourth, bamboozling the Miami defense to drain a superb stepback three-pointer from 26 feet as Boston closed out a brutal victory.
Game three in the series takes place in Boston on Saturday, and Smart is expecting a stiff Miami response.
"The number one and number two teams going at it, it's a grind," Smart said.
"We know they're coming to our house trying to get a win. We've got to protect our home court."